A volume of \(10 \mathrm{~m}\) l chlorine gas combines with \(25 \mathrm{~m}\) l of oxygen gas to form \(10 \mathrm{ml}\) of a gaseous compound. If all the volumes are measured at the same pressure and temperature, what is the molecular formula of compound formed? (a) \(\mathrm{Cl}_{2} \mathrm{O}\) (b) \(\mathrm{Cl}_{2} \mathrm{O}_{7}\) (c) \(\mathrm{ClO}_{2}\) (d) \(\mathrm{Cl}_{2} \mathrm{O}_{5}\)

According to Avogadro's Law, the volume of a gas is directly proportional to the number of moles it contains at a constant pressure and temperature. Mathematically, this can be represented as follows: V1/n1 = V2/n2 Here, V1 and V2 are the volumes of the gases, and n1 and n2 are the number of moles of the gases, respectively. We can use this equation to establish a relationship between the moles of reacting gases.

We are given that 10 ml of chlorine gas reacts with 25 ml of oxygen gas. Let's find the ratio of moles of chlorine to moles of oxygen reacting to form the compound: n1(V1) = n2(V2) Since we are only comparing the ratios, we can assume V1 = 10 and V2 = 25. Therefore, n1(10) = n2(25) n1 / n2 = 25 / 10 n1 / n2 = 5 / 2 The mole ratio of chlorine to oxygen is 5:2.

Now that we have the ratio of chlorine to oxygen moles, we can write the empirical formula of the compound: (Cl)x (O)y Here, x = 5 and y = 2. So, the empirical formula is Cl5O2.

The empirical formula Cl5O2 doesn't match any of the given molecular formula options. However, it may be possible that the actual molecular formula is a multiple of the empirical formula. Let's compare the moles of the compound formed with the moles of each of the given molecular formulas: Option (a) Cl2O: - Moles: 5 moles of Cl and 1 mole of O - This formula has the same ratio of 5:2 as determined earlier, so it matches. Option (b) Cl2O7: - Moles: 2 moles of Cl and 7 moles of O - This formula has a different ratio, so it doesn't match the empirical formula. Option (c) ClO2: - Moles: 1 mole of Cl and 2 moles of O - This formula has a different ratio, so it doesn't match the empirical formula. Option (d) Cl2O5: - Moles: 2 moles of Cl and 5 moles of O - This formula has a different ratio, so it doesn't match the empirical formula.

Based on the comparison with the given molecular formula options, the correct molecular formula for the compound formed is option (a) Cl2O.